Picking The Stars

Almost thirty-one year ago, a midshipman on his way to China met an old officer on the trans-Pacific steamer who gave him some very excellent advice: “Youngster, when you reach the Asiatic station get on the strictest and the tautest ship you can, for as the twig is bent so the tree will grow. And then take up something as a specialty. If you haven’t any originality, learn the equipment allowance list by heart, but learn something better than the other youngsters, know more about it than they do.” Thirty-one years ago, stars were not as well known as they are today. Many of the old navigators knew little or nothing about stars and depended entirely on the sun for their positions.

When that young midshipman reported on board ship on the China station and went to the chaplain for books on stars to study, he learned that the only book the chaplain had in the library was A Summer Evening Sky through an Opera Glass, a book prepared for a young ladies’ seminary. And the navigator had only the old standby: Lecky’s Wrinkles in Practical Navigation which contained a few sketches of some of the major constellations.

Now, thirty-one years later, there are so many star charts, star finders, diagrams, and gadjets for finding stars, that this article may appear to be superfluous; but, from time to time, requests have been received from officers asking that the method of “picking the stars” conceived almost thirty years ago, be published for general information.

It is very probable that some officers are familiar with this method. Certainly those officers who, as midshipmen, made their practice cruises on the old Hartford in the summers of 1903 and 1904, and those officers who served on the old Pennsylvania in 1905 and 1906 will remember it.

In explanation of the method, it will be necessary to state some astronomical axioms that you all know and then apply them in the solution of the problem.

You all know about the mean sun and why it had to be conceived, so I’ll not have to touch on that subject except to note that the movements of this mean sun are uniform, and the functions of this mean sun are tabulated along with all other astronomical functions in the Nautical Almanac and the Ephemeris.

The following functions are taken from the 1931 Ephemeris:

R.A.M.S. 23 March 23-58-04.6
R.A.M.S. 24 March 00-02-01.2

Therefore the mean sun passed the vernal equinox at about 12:00 on March 23, 1931. The exact time of passage was 11:42.

R.A.M.S. 22 September 11-59-34.4
R.A.M.S. 23 September 12-03-31.0

Therefore the mean sun passes the autumnal equinox at about 00:00 on September, 22. The exact time is 02:36.

The following functions are taken from the 1932 Ephemeris:

R.A.M.S. 22 March 23-57-07.68
R.A.M.S. 23 March 00-01-04.24

Therefore the right ascension of the mean sun will be zero at about 17:00 on March 22, 1932. The exact time will be 17:29.

From this it is apparent that the R.A. M.S. was zero at about 12:00 on March 23, 1931, and that it advances at the rate of two hours per month, again becoming zero at the next vernal equinox at about 17:00 on March 22, 1932.

As this scheme for “picking the stars” is done mentally, entirely without the aid of star charts, diagrams, pencil, or paper, whole numbers are used as they are sufficiently accurate approximations to insure accurate results within the possibilities of angle estimating.

It is seen that the R.A.M.S. advances at the rate of 2 hours per month, or 120 minutes per month. Assuming a 30-day month, this gives a rate of 4 minutes per day.

Check it and see how closely it agrees with the tables. For instance, at the end of six months the R.A.M.S. at this daily rate equals 12 hours, which jibes with the tables exactly.

In determining the R.A.M.S. for any date, it is therefore only necessary to count the number of whole months from March 23, allowing 2 hours for each, and then count the remaining days to your date and multiply by 4 minutes. Adding these two results gives you the exact R.A.M.S. for your date. Try it and see how simply it works.

As the mean sun is uniform in its movements, it is always in your meridian at noon time, in the western horizon at 6:00 P.M., under foot at the nadir at midnight, and in the eastern horizon at 6:00 A.M.

In other words, the mean sun moves uniformly through each quadrant in 6 hours or at the rate of 15° of arc each hour.

Keeping this in mind, it is very easy to determine the exact position of the mean sun at any hour of the night. For example: At 7:00 P.M. the mean sun is one hour below the western horizon. At 9:00 P.M.  the mean sun is three hours below the western horizon, or halfway to the nadir. At 2:00 A.M. the mean sun has advanced past the nadir by two hours and is 30° from it, at the same time being 60° below the eastern horizon.

Visualize a celestial circle passing through your zenith and nadir and through the east and west points of your horizon, in other words, your prime vertical. At different hours indicated, the positions of the mean sun are as shown in Fig. 1.

You now have a method of determining mentally exactly where the mean sun is at any hour of the day or night. You also have a method of determining exactly what the R.A.M.S. is for any day of the year. By applying the R.A.M.S. which you have determined mentally—no paper or pencil permitted—to the position of the mean sun at the instant you make your calculations, you can determine exactly the position of the first point of Aries, which is the position of zero hour’s right ascension, the point from which all right ascensions are calculated from 0 to 24 hours.

Imagine yourself facing north, standing at the center of a celestial circle passing through the east and west points of your horizon, and through your zenith, your prime vertical. See Fig. 2.

It is 9:00 P.M. on May 24, 1931. Visualizing yourself as indicated, you at once know that the mean sun is halfway down the quadrant below the western horizon. As it is May 24 you know that the vernal equinox has advanced since March 23, two months and approximately a half day. Therefore, the R.A.M.S. is 4 hours plus.

Still facing north, hold your left arm downward at an angle of 45° below the horizontal and you are pointing at the position of the mean sun. Then count around through the nadir the four hours right ascension of the mean sun and you find that the first point of Aries is one hour past the nadir. Having determined mentally the position of the first point of Aries, you are now in a position to determine the right ascension of any star in the heavens. For example: A star is halfway up in the western sky—Fig. 2. The angular distance from the first point of Aries to the western horizon is 1 hour to the nadir plus 6 hours to the horizon or a total of 7 hours. A star, No. 1, halfway up in the western sky is 3 hours above the horizon, therefore its right ascension is 7+3 = 10 hours. In the same way, the right ascension of a star, No. 2, in your meridian is 7 hours to horizon plus 6 hours to the meridian or 13 hours. In other words, at that instant, the right ascension of your meridian is 13 hours which is the local sidereal time.

And to continue, a star, No. 3, which is one-half up in the eastern sky, will have a right ascension of 13 + 3 = 16 hours.

Practice this method and you will be astonished at the closeness with which you can estimate the right ascension of any star in the heavens. Practice it first with stars you know until you feel some confidence in your ability to estimate angles of 15°, 30°, 45°, 60°, and 75°. Use both arms in making these estimates and note the positions of your arms for each angle. After having perfected yourself with stars you know, try it on stars you do not know and after awhile you will be very agreeably surprised at the facility with which you can determine the right ascensions of them all.

You are now in a position to estimate the right ascension of any star with accuracy and can proceed with the next step.

The next step is quite simple and much shorter to explain. We all know that the angle of elevation of the elevated pole above the horizon equals the latitude of the observer. Note the direction of north by your standard compass unless you can see the pole star. Face to the eastward and hold your left arm pointing to north and at an angle above the horizontal equal to your latitude. You are pointing to the earth’s elevated pole. Then hold the right arm up over your head keeping it at right angles to the left arm. Sweep it back and forth from east to west. Your right arm, if it could be extended, would scribe a circle on the sky which is the celestial equator, from which the declination of all celestial bodies is measured.

You have now determined the bench mark or reference plane for measuring declination. Keeping the right arm pointed toward the celestial equator, move the left arm till it points to the star whose identity is in question.

The angle between your two arms represents the declination of the star. If its declination is south, you will have to shift your arms for comfort in estimating the angle, pointing the left arm to the celestial equator and using the right arm to point to the star.

This is the method for determining the declination of stars before they reach the meridian.

After the stars have passed the meridian, your positions must be reversed. After determining the direction of north, face to the westward, and hold the right arm above the horizon at an angle equal to the latitude and describe the circle of the celestial equator with the left arm held overhead and at right angles to the right arm.

Fig. 3 shows the declination determination of three stars, two north of the celestial equator and one south.

After practicing this method on stars that you know, and of whose coordinates you are certain, try it on unknown stars and you will quickly develop your angle sense in estimating the angular distance between the celestial equator and the stars.

Having mastered these two methods: (1) to determine the right ascension of any star; (2) to determine its declination, you are now ready to pick any star in the heavens.

You may have asked yourself the question: What use is this when I can see the other stars and can always get one that I know? Perfectly true, but sometimes you cannot see other stars due to clouds, or the stars you know may not be in good positions for navigational sights.

In either case, you can take an observation of the star whose position is best suited for your purpose, or it may be the only star you can see at that time; and after having obtained its altitude, you can then quickly determine mentally its identity. The sight may save you and the ship considerable embarrassment if not disaster.

I have frequently found it of great assistance to take a couple of stars, one on either beam. Their resultant lines of position show you where your course is leading you. One taken ahead or astern will show you how far along your course you have traveled. In approaching a coast at night, particularly if the coast is not well lighted, the importance of such sights cannot be overestimated. If you have the time and inclination, you should also take one star on the prime vertical and one for latitude. With these five sights taken with a good horizon, your position is accurately fixed and you can stand in on even a poorly lighted coast with confidence.

Having determined mentally the right ascension and the declination of the star, and having observed its altitude—for working the sight—and having noted its approximate azimuth, you can quickly select the proper star in the Nautical Almanac. You will find after a little practice that your estimated right ascension and declination will approximate very closely the recorded right ascension and declination in the Nautical Almanac. The magnitude of the star will also aid you in identifying the star in the tables as it is very seldom that you will find two stars with approximately the same coordinates and of equal magnitude, particularly among those stars known as navigation stars. And you are not interested in the fainter stars.

This method has been repeatedly used both north and south of the equator with equal success both by me and by other officers to whom I have explained the method during the past twenty-five years.

After some practice with this method of “picking the stars,” you will subconsciously remember the coordinates of some of the stars and this knowledge will aid you materially in your study of the constellations.

I have found it of great assistance to divide the heavens into sectors:

Zero hours right ascension line

A line from Polaris just clear and to the right of Beta Cassiopeia (Caph) is the line of zero hours or 24 hours right ascension. This line continued to the southward about 30° of arc will just clear Alpha Andromedae (Alpheratz).

Six hours right ascension line

A line from Polaris just clear and to the left of Beta Auriga (Menkalinan) and Gamma Auriga is the line of 6 hours right ascension. This line continued on through Delta Auriga—a fourth magnitude star— gives you an absolutely straight line, parallel to and very close to the line of 6 hours right ascension. This 6-hour line passes to the left of Alpha Orion (Betelgeuse).

Twelve hours right ascension line

The line from Polaris passing between Gamma Ursa Major (Phecda) and Delta Ursa Major (Megrez) is the line of 12 hours right ascension. The two stars in Ursa Major referred to are the third and fourth stars in the big dipper; the first two stars, Alpha and Beta, being the pointers to Polaris. This line of 12 hours right ascension passes only 15' of arc to the left of Beta Leonis (Denebola) which is the second largest star in the constellation of Leo, and after crossing the celestial equator and passing to 20° south declination, just clears the star forming the heel of the mast of the ship’s spanker in the constellation of Corvus.

Before passing on to the next quadrant, attention is invited to the position of the pointers of Polaris, Alpha, and Beta, Ursa Major, which are exactly on the line of 11 hours right ascension. By means of these two stars, it is very easy to tell the time of night without the use of paper or pencil, book or watch, and after a little practice you can tell the time within 5 minutes.

Eighteen hours right ascension line

The line of 18 hours right ascension is not so well defined by any large star. However, a line from the second star in Ursa Minor; that is, the nearest star to Polaris, passing slightly to the right of Polaris and continued in the opposite direction, will mark the line of 18 hours right ascension. This 18-hour line will pass within 0.5° of arc of the large star Alpha Lyra (Vega). If these lines outlining the four quarters are memorized they will very materially aid you in your star study.

There are other stars which also are of considerable assistance if their right ascensions are memorized. For instance, Alpha Pegasus (Markab) and Beta Pegasus (Scheat) are exactly on the line of 23 hours right ascension. In other words, these two stars on one side of Polaris and the two pointers of Ursa Major on the other side are in an exact straight line. Remembering their right ascension, these two stars can also be used for telling the time at night very accurately—just like the two pointers of the big dipper.

Now having explained how to pick the stars accurately and quickly, I will show one example of the practical application of the method.

In the late afternoon of June 23, 1931, you wish to know what stars you can use that evening at about seven o’clock. Fig. 8. You know that the right ascension of the mean sun is 6 hours. You therefore know that at 7:00 P.M., when the mean sun is one hour below the western horizon, and with a right ascension of 6 hours, the first point of Aries will be 1 hour past the nadir. With that as your reference point, you can calculate that any star with 7 hours right ascension will be in the western horizon and a star with 19 hours right ascension will be in the eastern horizon; also that the right ascension of your meridian at 7:00 P.M. will be 13 hours which is your local sidereal time.

As it is not good practice to observe stars within an hour or an hour and a half of the horizon, your practical arc of observation is further restricted by an hour and a half approximately at the eastern and western limits, therefore your effective stars are between right ascension 8.5 hours and 17.5 hours. Your lowest altitude best star to the westward is therefore Regulus and to the eastward is Rasalhague. An hour later you will have Vega in excellent position to the eastward. At the same time (7:00 P.M) Spica will be almost on the meridian to the southward.

Using the same time as an example, look in the Nautical Almanac and see what stars are included between 8.5 and 17.5 hours right ascension. You will see that Regulus is about halfway up in the western sky, that Denebola is about an hour and a quarter past the meridian, that Spica is about twenty minutes to the eastward of the meridian, Arcturus is about an hour to the eastward of the meridian, Alphacca an hour beyond Arcturus, and Antares an hour beyond that.

Knowing your latitude, you know the declination of your zenith, and therefore you can determine whether the declination of any star renders it unsatisfactory for your observation that night.

Having thus determined what stars you can use that night and their positions in the sky, you are fully prepared to go on deck at seven o’clock and make your observations without any loss of time as you know exactly where to look for each star.